I'm going to be installing a patio door between 10-12ft wide, which will knock out quite a few studs. The wall supports a second story above. Since this is in a basement with a low ceiling, I'd like to have the narrowest header that would be sufficient to support that size of a door opening. Ideally, it would be no more than 6", and preferably closer to 4". I'd be willing to use steel I-Beams if it were possible to, but if I have to use wood for the header, what would be recommended? Also, if steel I Beam recommended for header, how can I attach the I Beam header to the supporting studs? Any suggestions much appreciated.

I can't give specifics, but look at engineered lumber. basicaly a wood I beam. Just make sure it is big enoughacording to local codes. You do not want it sagging out in the middle.
There are also connection pieces to make a wood steel connection. Look for egn. data on their websites

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[FONT="Franklin Gothic Medium"][SIZE="3"][B]Everyone is entitled to their own opinion, but not their own facts[/B][/SIZE][/FONT]

Make sure you check with the loco building dept. They will have some ideas as how far to span and what size. Don't forget you are in earthquake country and need to get the correct connections for your seismic area. Any small tremors could end up with you not having a house,or worse.
I don't want to be the bad guy here but in my job I see to many things that happen because someone was trying to be smarter than the system in place to help them from themselves.
The reason I am so crotchety today is there was a failure of a deck in our area recently. Someone went to the big box store and built themselves a deck with no permits.
10 feet of the ground with 2 4x4 posts and no angle supports and a couple of nails into the house.
No fatalities, didn't even make the news...but he saved some money and knew just enough to be dangerous.

Right on Inspector D.
Check with the local building authority. There are several options of engineered lumber though: Glu-lam beams are made of 2"x? (whatever width works best; the individual pieces are laid flat then glued and nailed or clamped together with a camber in them (a hump or bow that settles out under load, rather than sagging). Another good one is made of OSB and glued up to the thickness required to handle the load. An old one I have used is sandwich a piece of 1/4" steel plate between two 2by's bolt it every foot staggering bolts to top and bottom and both locations on each end.
Glenn

On second thought, Greg, you should look at the size of your floor joists and the Band beam at the end of them. You may have double 2x10s up there already and all you would need to do is fill in the void above the door.
Glenn